How do you solve #4x+y=13# and #2x-y=5#?

1 Answer
Aug 1, 2015

Answer:

Add the 2 equations together to get a third equation with the #y# term eliminated; solve for #x#; replace #x# in one of the given equations with the solution to find #y#
#(x,y) = (3,1)#

Explanation:

[1]#color(white)("XXXX")##4x+y=13#
[2]#color(white)("XXXX")##2x-y=5#

Add [1] and [2] together
[3]#color(white)("XXXX")##6x=18#

Divide both sides by #6#
[4]#color(white)("XXXX")##x=3#

Substitute #3# for #x# in [1]
[5]#color(white)("XXXX")##4(3)+y=13#

Simplify
[6]#color(white)("XXXX")##12+y=13#

Subtract #12# from both sides
[7]#color(white)("XXXX")##y=1#